Apparatus for compensating quadrature resolved unbalance components



Y W. F. KING APPARATUS FOR CDMPENSATING QUADRATURE Feb. l0, 1959 2,872,819 RESOLVED UNBALANCE COMPONENTS 5 Sheets-Sheet 1 Filed April l. 1954 ir' 2 fifi w a...

ATTORNEY Feb.

. W. F. APPARATUS FOR COMPENSATING QUADRATURE RESOLVED Filed April 1. 1954 KING -UNBLANCE.' COMPONENTS HNE/FIFA s sheets-sheet 2 INVENTOR B'Y y wwf@ ATTORNEY Feb. 10, 1959 KING 2,872,819

' W. F. APPARATUS FOR COMPENSATING QUADRATURE RESOLVED UNBALANCEZ COMPONENTS Filedlpril 1, 1954 SSheets-Sheet 3 o .J5 ao 4f: a f5 sa A/Yazf of a/vaAA/y (e) INVENTOR ATTORNEY Bf @@/Qw States url APPARATUS FOR COMPENSATING QUADRA- TURE RESOLVED UNBLANCE COMPONENTS Application April 1, 1954, Serial No. 420,230

Claims. ('Cl. 715-462) This invention relates to automatic balancing installations and, more particularly, to apparatus for compensating quadrature or conjugately resolved components of a total unbalance quantity to permit balance corrections to be made at points spaced other than 9() `degrees apart.

The invention is specially suited ifor use in automatic balancing installations in which Ithe total imbalance-in a selected transaxial plane of correction of a dynamically unbalanced rotating body is vectorially resolved into 'two components and a balance correction performed therefor at two predetermined points spaced a fixed angular distance apart on the surface of the body. An automatic balancing installation of this character adapted to effect unbalance determinations and balance corrections in elongated rotating bodies such as crankshafts and the like is shown and described in Patent No. 2,783 ,649, issued March 5, 1957 in the name of Lawrence F. Hope, `and assigned'to the present assignee. In this apparatus a rough balance correction is performedat two quadrature related, transaxial coplanar points on the cheek of selected counterweights of an engine crankshaft.

lt is sometimes desirable to perform such balance corrections at angles other than 90 degrees apart, as where it is desired to perform a subsequent finish or assembly balance of a crankshaft after it has been installed in an engine in order to correct for 'any unbalance effects thereon due to other parts of the engine. In such event a small amount of rough unbalance, say about 0.5 1oz-inches, is intentionally left in the shaft in order to control within limits the approximate location lof the finish assembly unbalance, which occurs at a Variableuangle relative to an axial reference plane of the shaft. Therefore, it is desirable that the points at which the rough balance vcorrection is performed be spaced as widely apart as 'possible in order to provide a long unobstructed sector on the cheek of the crankshaft and to assure that the finished balance correction will fall somewhere between the rough balance correction points.

Accordingly, the present invention has for its general object to provide apparatus for compensating quadrature resolved components of an unbalance quantity to permit balance corrections at angles different from 90 degrees or 1r/2 radians.

The manner in which the foregoing is accomplished will appear from the following detailed description and drawings in which:

Fig. 1 is a schematic and block diagrammatic showing of a form of balancing apparatus in which the present invention may be employed;

Figs. 2 and 7 are vector diagrams useful 'in understanding the principle of the present invention;

Figs. 3 and 6 are curves relating to the theory of the present invention;

Fig. 4 is a part of apparatus of the type illustrated in Fig. l; and

Fig. 5 is a modification of the apparatus of Figs. l and 4 in accordance with present invention.

Referring t-o Fig. l of the drawings, the body to be balanced is shown as a crank shaft 1t) mounted in a fixture 12 which includes a pair of resilient or oscillatable supports 14, 16 that permit vibration of the ends of the shaft in an axial plane thereof. The shaft is coupled through a 2,872,819 remates rea. to, tas-a suitable coupling arrangement i8 to be driven by a constant speed drive motor 20. `Coupled to the supported ends of the shaft is a mechanical nodal bar 22 having an electrical pickup 24 positioned at Vone of the mechanical nodes thereof.

No attempt has been made to show any particular construction of mounting supports and coupling for the shaft and the nodal bar, the drawings being for the most part `of a diagrammatic nature to bring out principles of operation rather than particular details of construction. However, reference is made to U.'S. Patent 2,293,371 in the name of T. C. Van Degrift assigned to the present assignee illustrating and describing a suitable mounting and nodal bar construction which can be adapted for use in the foregoing apparatus.

The electrical pickup 24jgenerates an alternating current signal representative of the total unbalance quantity in` a selected correction plane through a counterweight 11 of the shaft. The pickup signal is applied over conductors 26, 27 and amplified in a suitable amplifier 28 from which it is applied over conductors 29, 30 to a commutation or equivalent integrating arrangement 32a. Following the amplifier 28, the numerical designation of the elements of the balancing installation herein illustrated will be accompanied by the lower case letters a or b whereby they may bev identified with the particular unbalance component a or b, as in Fig. 2 for example, being determined thereby.

The commutation arrangement 32a may include an input transformer 34a having a center-tapped secondary winding 36a, a relay switching element 33a having a twoposition switch arm 49a and an activating coil 42a euergized from a D. C. source 44a through a mechanical commutator 46a comprising one or more continuous rings 48a and a pair of split rings Sila, 52a separated by an insulating segment 54a. The commutator 46a is coupled to rotor shaft 21 of the drive motor to be driven in synchronism'with crank shaft 10 and has a pair of stationary brushes 56a, Sdu associated with the continuous ring and the two split rings, respectively. The commutator 46a functions to interrupt the energization of the relay activating coil 42a for a 180 degree interval of the pickup signal so as to produce a commutated or interrupted wave the average value of which is proportional to the amplitude of the pickup signal and the angular location of the co-mmutator brushes 56a, 58a relative to Vthe axial plane containing the total unbalance. A suitable form of electronic integrating device that may be employed in place of the electro-mechanical commutation arrangement herein is illustrated in Patent No. 2,783,907, issued April 9, 1957, in the name of the present inventor and assigned to the present assignee.

The output of the commutation arrangement is applied over conductors oil@ 62a to a ripple smoothing filter 64a and then to a self balancing amplitude comparison circuit 66o comprising an adjustable potentiometer device n connected across a standard reference D. C. source 79a, a conventional servo amplifier 72a and a two phase servomotor 74a. The rotor shaft 76a of the servomotor '74a is coupled to the adjustable arm 69a of the potentiometer device and to an adjustable drill stop setting device 78a that may be electrically or mechanically associated with an adjacent or remotely located drilling organization (not shown) or equivalent apparatus with which the balance correction may be performed.

The filtered signal appearing between the conductors Stia, 32ay represents the amplitude of the a component of the total unbalance U of Fig. 2 and is compared in thev amplitude comparison circuit 66a against that portion of the known potential of the standard reference source 70a appearing between conductor 80a and the potentiometer arm 69a of the potentiometer device. The net il u difference signal between these quantities is applied as an error signal over loop closing conductors 82a and 84a to the input of the servo amplifier 72a whose output is applied to the control phase winding of the twophase servo motor to control the direction and extent of rotationthereof. The angular rotation of the servo motor 74a is proportional to the amplitude of the unbalance component and may be determined from a suitable pointer 86a mounted on the servomotor shaft 76a and a scale 88a calibrated in oz.inches on the stator casing thereof.

Another commutator or equivalent device 46h having brushes Sb, 58b spaced 90 degrees relative to the brushes of commutator 46u is mounted on theshaft 21 of the drive motor 2G for association with a commutation arrangement, lilter and amplitude comparison circuit similar to that associated with commutator 46a and serves to provide an automatic determination of the other unbalance component b conjugately or orthogonally related to the unbalance component a. The above described arrangement for obtaining both of the unbalance components is shown somewhat more completely in the diagrammatic illustration of Fig. 4 in which the blocks labelled Component a and Component b inthe branch circuits include the above described commutating arrangement and filter. Instead of employing separate reference sources for the balancing potentiometers 63a and 68b, a single reference source may be employed for both of the potentiometers, the high potential sides of which may be connected to the positive terminal of the reference source whose negative terminal is grounded.

In accordance with the present invention a compensating cross-correction network is added to the apparatus of Figs. l and 4 to permit the drilling of balance holes at included angles other than 90 degrees. Before proceeding with the description of the compensating network, the following analysis is given to illustrate the theory underlying the invention and as applied to a specific example where the included angle is 100 degrees.

The vector diagram of Fig. 2 shows an unbalance force U at an angle 0 (theta) resolved into two sets of component a, b and a', b' having included angles of 90 degrees and 100 degrees, respectively, therebetween. Methematically these components may be represented by the following equations:

d 68b through suitable voltage dropping resistors 17001 and 7b, as shown in Fig. 5. The arms l69a and 169b of the auxiliary potentiometers are operatively coupled to be driven from the shafts 76a and 76b of the servomotors 74a and 74b, respectively. Electrically, arm T1690 of auxiliary potentiometer 16881 is connected over conductor 184b to one terminal of servo amplifier 72b, while arm 169b of auxiliary potentiometer 168b is connected over conductor 18401 to the corresponding terminal of servo amplifier 72a. The auxiliary potentiometers 16301, 168b thus are mechanically associated with the servomotor drive of a respective one of the component networks but are electrically cross-connected or assoeiated with respectively opposite component networks. Rotation of the servomotor 74a in the component 'a circuit will inject a compensating voltage and cause a change in voltage in the component b circuit, and similarly with servomotor 74b. These compensating voltages (ka and kb) are a fixed percentage of the main balancing voltages a' and b appearing between the respective arms 69a and 69h and ground of the main potentiorneters 68a and 68b and thus either add or subtract a percentage voltage to the opposite component circuit for a given change in either of the main potentiometers. This modified circuit would be useful in adding the extra drill depth required for balancing at 100 degrees provided that the required increase in magnitude of one balancing force due to the drilling angle change were proportional to the required balancing force at 100 degrees of the other component, or, stated mathematically, provided that the following relations should apply:

a=U cos 0 1) were computed, since these values would be indicative b=U sin 0 (2) of the relationship between the change in balanclng force sin (0.1.5) magnitude with the change in drilling angle and the total I'=U[00S (@'l'5)+ -tan 80 (3) 50 correction required for the respective components. These (95 0) ratios are tabulated in Table 2 below, and a plot of the SID 4 ratlo 0 Ulcos (95 91+ tan 80., a' a Assuming values of 0 in 15 degree increments between -b-, 0 and 90, the following tabulation of figures con- 55 tained in Table 1 are obtained: 1s shown m Fig. 6.

Sill 95-0 bl 9 0 00s@ 5 sin @+5 @1 0-h a' 00895-0 81095-9 C320 Sin)0 Tan 80 Tan 80 Fig. 3 shows the a and a components taken from l r nl a N b Table l plotted as a function of the angle 0 of the total A1181@ a -a b -b b, T unbalance force U. From these curves 1t may be noted that the required correction increment due to the W1der o. 01 l 6 0. 0885 0 1311 00875 angle is not constant, but varies with the angle 0. g'g s gg 8.3% g

The cross correction compensating circult 1n accord- 0:0708 0:0708 3:3352 gggg 0.0824 0. 0540 ance wlth the present invention employs a pair of aux 0.0885 0.0341 0.0885 0.0982 1l1ary potentiometers 16801 and 168b which are connected 7 0 0885 0 0116 0 0875 13u across respective main balancing potentiometers 68aand 5 From this table a value of 0.09 was chosen as an average value of the above ratios representing the factor k o f Equations 5 and 6. By making the voltage dividing resistances 170e, 170b ten times as large as the resistance of the auxiliary potentiometers 168:1, 168b, the circuit of Fig. 5 will inject a compensating voltage into one component network equal to 9% of the main balancing voltage (a or b) of the othercomponent network and thus correct or compensate the quadrature related signal components rz and b appearing between conductors 80a, 82a and S0b, 82b of Fig. 5 to yield a close approximation for a balance correction to be performed at the larger included angle of 100 degrees. The error due to using this method of using a xed value for the quantity k to approximate a and b is shown in Table 3 below based on a l2 oz.in. unbalance. The error in a' would be a' (a}.09b), where fr' is taken from Table l.

As shown in Table 3, the absolute and percentage error due to using a constant percent correction is of small enough magnitude to make the method usable.

Another approach may be made to the problem by considering Fig. 7. Compo-nent a is rotated counterclockwise to the A axis, which is vdisplaced by an angle (phi) of 5 degrees from the vertical A axis. The vector (b sin qa) corresponds to an addition of a percentage of vector b to vector la, which in the specific case discussed is 0.087 or 8.7% of the length of vector b. This vector quantity plus vector a falls short of equalling vector a', the required correction, by the slight error indicated on the drawing. it will be seen that the correction is always less than that required for exact balance. For this reason, an average value of 0.09 or 9% was chosen to reduce the error and make it both a plus and minus one. The same analysis may be performed on the B axis with corresponding results.

With the system of cross correction thus described, drilling balance holes at an angle of 100 degrees, rather than 90 degrees, will produce an error of less than 0.4% balance. In terms of a l2 ounce-inch correction this error would be less than 0.05 ounce-inch, which is well within the correction limit requirements of most industrial balancing applications. As an academic matter, where an extremely high degree of accuracy is sought to be obtained, the variable nature of the incremental compensating quantity could be accounted for by various expedients, as by using a cam having a configuration 'corresponding to the variable quantity and associated follower in the mechanical couplings or linkages between the servo motors and the arms of the auxiliary potentiometers.

While the invention has been described as applied to a specific included angle of 100 degrees, the method of analysis can be extended to and the compensating apparatus employed to perform balance corrections at other angles.

I claim:

1. The combination with apparatus for analyzing an unbalance force of an unbalanced rotating body into two components and including vibration pickup means developing an electrical signal having characteristics related to said unbalance and component analyzing means resolving said unbalance force into two quadrature relatedcomponents, said analyzing means being connected to said vibration pickup means and having a pair of branch circuits providing signal outputs corresponding in magnitude to said quadraturerelated components, of means for modifying said quadraturerelated components to permit balance correction for said 4unbalance .force at a pair of fixed points 'on .said body having an in eluded angle different from degrees therebetween comprising an adjustable compensating network having a pair of circuit branches ycross-connected-in the output circuits `of said component analyzing means.

2. In combination, a source of potential and a pair of amplitude comparison circuits, each of saidcircuitshaving a pair or input terminals adapted to be interconnected with signal sources, a pair of .main balancing potentiometers each connected across .said potential sour-ce and having an adjustable `arm connected to one of the input terminals'of a respective one kof said ampli tude comparison circuits, means responsive .to a signal and operatively interconnected with said arm to be effective to actuate said arm in response to said signal, and a pair of auxiliary potentiometers each connected across said potential source and having an adjustable arm mechanically coupled to the adjustable arm of a main balancing potentiometer in one of said amplitude comparison circuits for movement therewith and electrically connected to supply a voltage in a circuit connected to the other input terminal of the opposite amplitude comparison circuit.

3. Apparatus for analyzing an unbalance force of an unbalanced rotating body into two components comprising, in combination, vibration pickup means developing an electrical signal having characteristics related to said unbalance force, component analyzing means resolving said unbalance force into a pair of quadrature related components, said analyzing means being connected to said vibration pickup means and having a pair of branch output circuits providing signal outputs corresponding in magnitude to said quadrature related components, a separated servo controlled balancing system for each of said branch circuits including a main balancing potentiometer connected in differential opposed circuit relation with the said signal output of a respective one of said branch circuits, a servo amplifier connected to receive the difference signal between said main balancing potentiometer and the signal output of a branch circuit, and a servomotor controlled from said servo ampliiier and coupled to adjust the output of said main balancing potentiometer, and means for modifying said quadrature related components to permit balance correction for said unbalance force at a pair of xed points on said body having an included angle different from 90 degrees therebetween, said means including a pair of auxiliary potentiometers connected across respective ones of said main balancing potentiometers, each of said auxiliary potentiometers being individually mechancally coupled for adjustment by the servomotor associated with the main balancing potentiometer across which each auxiliary potentiometer is connected and being electrically connected to inject a compensating voltage in the branch circuit in which the other main balancing potentiometer is connected.

4. The combination with apparatus for resolving an unbalance force of an unbalanced rotating body into two components and including vibration pickup means developing an electrical signal having characteristics related to said unbalance and component analyzing means resolving said unbalance force into two quadrature related components, said analyzing means being connected to said vibration pickup means and having a pair of branch circuits providing signal outputs corresponding in magnitude to said quadrature related components, of means for modifying said quadrature related components to permit balance correction for said unbalance force at a pair of xed points on said body having an included angle different from 90 degrees therebetween, said modifying means comprising a source of potential and a pair of amplitude comparison circuits each having a pair of input terminals, a pair of main balancing potentiometers each connected to said potential source and having an adjustable arm connected to one of the input terminals of a respective one of said amplitude comparison circuits, and a pair of auxiliary potentiometers each connected to said potential source and having an adjustable arm mechanically coupled to the adjustable arm of a main balancing potentiometer in one of said amplitude comparison circuits and electrically connected to supply a voltage in a circuit connected to the other input terminal of the opposite amplitude comparison circuit.

5. In combination, a source of potential and a pair of amplitude comparison circuits, each of said circuits having a pair of input terminals, a main balancing potentiometer in each of said circuits connected across said potential source and having an adjustable arm connected to one of the input terminals in its circuit, a servo amplier in each of said circuits having an input and an output connected to a servomotor, each of said servomotors being mechanically coupled to the adjustable arm of the main balancing potentiometer inthe amplitude com# References Cited in the le of this patent UNITED STATES PATENTS 2,243,379 Johnson May 27, 1941 2,293,371 Van Degrift Aug. 18, 1942 2,363,373 Werner Nov. 21, 1944 2,500,013 Svensson Mar. 7, 1950 2,636,381 Hagg Apr. 28, 1953 2,706,399 Federn Apr. 19, 1955 2,720,781 Federn Oct. 18, 1955 UNTTED STATES PATENT oEETCE CEBTIFlCATE OF 'CORREGTlON Patent No. 2,872,819 February lO, 1959 William F. King n'ted specification s in JShe -pri b the said Letters at error` appear tion and 'bha rtified th d patent requiring correo s Corrected below.

lt is hereb ce oi the above 'numbere Paten-b should read a 2,783,907" read Patent No. A

Methematioally read Mathematicl -aseparate' Patent No. for Separatew rea Column 2, line' A9, for 2,787,907 column 3, line A4, cally Column o, line 37, for

ed and sealed this 7th day of July l959.

Sign

(SEAL) Attest: KARL H' MINE A ROBERT o. WATSON Attesting Officer v Commissioner of Patents 

